Anderson–Darling test

The Anderson–Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution. In its basic form, the test assumes that there are no parameters to be estimated in the distribution being tested, in which case the test and its set of critical values is distribution-free. However, the test is most often used in contexts where a family of distributions is being tested, in which case the parameters of that family need to be estimated and account must be taken of this in adjusting either the test-statistic or its critical values. When applied to testing whether a normal distribution adequately describes a set of data, it is one of the most powerful statistical tools for detecting most departures from normality.K-sample Anderson–Darling tests are available for testing whether several collections of observations can be modelled as coming from a single population, where the distribution function does not have to be specified.

In addition to its use as a test of fit for distributions, it can be used in parameter estimation as the basis for a form of minimum distance estimation procedure.

The test is named after Theodore Wilbur Anderson (born 1918) and Donald A. Darling, who invented it in 1952.

The Anderson–Darling and Cramér–von Mises statistics belong to the class of quadratic EDF statistics (tests based on the empirical distribution function). If the hypothesized distribution is ${\displaystyle F}$, and empirical (sample) cumulative distribution function is ${\displaystyle F_{n}}$, then the quadratic EDF statistics measure the distance between ${\displaystyle F}$ and ${\displaystyle F_{n}}$ by

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